10436 ÷ 4 = 2609 R0
Alright, let's work through the division of 10436 by 4 step by step.

Step 1:
4 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 1 to get 1.
Bring next digit (0) of the dividend behind the 1 and repeat the process: 10 / 4

Step 2:
4 goes into 10 2 times with a remainder of 2.
Write down 2 as next digit of of the result. 
Result so far: 2
Subtract 8 from 10 to get 2.
Bring next digit (4) of the dividend behind the 2 and repeat the process: 24 / 4

Step 3:
4 goes into 24 6 times with a remainder of 0.
Write down 6 as next digit of of the result. 
Result so far: 26
Subtract 24 from 24 to get 0.
Bring next digit (3) of the dividend behind the 0 and repeat the process: 3 / 4

Step 4:
4 goes into 3 0 times with a remainder of 3.
Write down 0 as next digit of of the result. 
Result so far: 260
Subtract 0 from 3 to get 3.
Bring next digit (6) of the dividend behind the 3 and repeat the process: 36 / 4

Step 5:
4 goes into 36 9 times with a remainder of 0.
Write down 9 as next digit of of the result. 
Result so far: 2609
Subtract 36 from 36 to get 0.

The final result is 2609 with a remainder of 0.